Simplify 3 \(^{n − 1}\) x \(\frac{27^{n + 1}}{81^n}\)
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Correct Answer: Option B
Explanation:
3\(^{n - 1}\) x \(\frac{27^{n + 1}}{81^n}\)
= 3\(^{n - 1}\) x \(\frac{3^{3(n + 1)}}{3^{4n}}\)
= 3\(^{n - 1 + 3n + 3 − 4n}\)
= 3\(^{4n − 4n − 1 + 3}\)
= \(3^{2}\)
= 9
3\(^{n - 1}\) x \(\frac{27^{n + 1}}{81^n}\)
= 3\(^{n - 1}\) x \(\frac{3^{3(n + 1)}}{3^{4n}}\)
= 3\(^{n - 1 + 3n + 3 − 4n}\)
= 3\(^{4n − 4n − 1 + 3}\)
= \(3^{2}\)
= 9